Auger-electron cascades in diamond and amorphous carbon

We have analyzed cascades of secondary electrons in diamond and amorphous carbon generated by the thermalization of a single Auger electron. The elastic electron mean free path was calculated as a function of impact energy in the muffin-tin potential approximation. The inelastic scattering cross section and the energy loss of electrons (expressed in terms of the differential inverse mean free path) were estimated from two “optical” models that utilize the measured dielectric constants of the materials. Using these data, a Monte Carlo model describing the time evolution of the cascade was constructed. The results show that at most around 20–40 secondary cascade electrons are released by a single Auger electron in a macroscopic sample of diamond or amorphous carbon. Consideration of the real band structure of diamond reduces this number further. The release of the cascade electrons happens within the first $100$ fs after the emission of the primary Auger electron. The results have implications to planned experiments with femtosecond x-ray sources.